I had a similar problem at my previous house. Except for the HOA part, we didn't have one. My solution was twofold. generally I could manage a modified 3 point (30 point?) turn using the driveways at the end of the cul-de-sac. You mention they are empty, so that seems like it could be an option. Pull in their driveway then back out the other way.
Other option I did a few times was just back it in the whole way. I knew I could do it since I had to back it out more than once when there was no way to turn around lol.
I would NOT call the HOA. Glass houses and all that stuff, burning bridges with neighbors is generally not a good idea if it can be at all avoided.
